The invention relates to a single lens having one spherical and one aspherical refractive surface. Such a lens, briefly referred to as a mono-aspherical lens, is known, for example, from British Patent Specification No. 1,499,861. The known mono-aspherical lens has a small numerical aperture and a small diffraction-limited field.
A conventional lens having two spherical surfaces produces an image of an axial point, which image is not diffraction-limited, especially at larger numerical apertures. If one surface of the lens is made aspherical a perfect (aberration free) image of the axial point can be obtained. Making only one surface aspherical does not, however, guarantee a high image quality of non-axial object points.
In order to strictly satisfy the Abbe sine condition it is known, for example, from British Patent Specification No. 1,512,652 to make both refractive surfaces of the lens aspherical.
Surprisingly the Abbe sine condition can be met substantially for mono-aspherical lenses having a large numerical aperture. To achieve this a suitable lens shape should be selected from the multitude of possible mono-aspheres. The choice of the lens shape with a maximum diffraction-limited field demands minimization of coma. By means of the third-order aberration theory it is possible to calculate for which lens shape third-order coma disappears in the case of a mono-aspherical lens whose focal length, refractive index, thickness and positions of the object plane and image plane are given.
It is found that for large numerical apertures (NA22 0.25) the third-order aberration theory is inadequate. Then, in order to obtain mono-aspherical lenses with a large diffraction-limited field, a specific amount of third-order coma has to be accepted; these requirements seem to be conflicting.